Rewrite as a simplified fraction. ${2.\overline{14} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 214.1414...\\ 1x &= 2.1414...\end{aligned}}$ Subtracting the two equations, we have: ${99x = 212}$ ${x = \dfrac{212}{99}} \text{or} {2 \dfrac{14}{99}}$